Series solutions to linear integral equations

Linear Volterra-type integral equations with kernels having a series expansion in the first variable have series solutions with coefficients given iteratively. Their resolvents may be expanded likewise. The associated homogeneous equation Kf=f generally has Frobenius series solutions when the kernel is singular, whereas Kf=0 generally has such solutions regardless of singularity: the proviso in each case is that associated “indicial equation” has solutions.